Recovering a Time‐Dependent Diffusion Coefficient From Flux Data in a Fractional Diffusion Model With a Higher‐Order Boundary Condition

ABSTRACT We study an inverse problem for a time‐fractional diffusion equation with a Robin condition at and an eigenparameter‐dependent higher‐order boundary condition at . For the direct problem we prove existence, uniqueness, and regularity of mild solutions. For the inverse recovery of a positive time‐varying coefficient , we introduce a monotone nonlinear operator whose fixed points correspond to data‐consistent coefficients. Monotonicity yields uniqueness, and under mild assumptions the associated fixed‐point (‐) iteration is monotone, bounded, and convergent. A modal discretization with L1 time stepping implements the iteration efficiently. Numerical experiments corroborate the theory and examine robustness to noise and the effect of the fractional order .